Hello, Selma,
The first thing I'll do is put the equation into the form y = mx + b. This will give me the slope, m, and b, the y intercept (the value of y when x=0).
y-9=(2/3)(x+7)
y-9 = (2/3)x + (14/3)
y = (2/3)x + (14/3) + 9
y = (2/3)x + (14/3)+(27/3)
y = (2/3)x + (41/3)
y = (2/3)x+ 13 2/3
The slope of the line is (2/3) and the y intercept is 13 2/3
It is the slope we're interested in. Parallel straight lines have the same slope, so the line we want will also have m=(2/3).
Let's make a parallel line by using the same slope:
y = (2/3)x + b
Looking good, but we still need b. We are in luck, because we know the point (2,3) in on the line we seek. Put these values into our new equation and solve for b.
y = (2/3)x + b
3 = (2/3)*2 + b
b = 3 - (4/3)
b = (5/3)
The equation of a line that is parallel and goes through (2,3) is thus:
y = (2/3)x +5/3
Bob
